Studies on the role of memory as a predictor of reading time latencies (1) differ in their predictions about when memory effects should occur in processing and (2) have had mixed results, with strong positive effects emerging from isolated constructed stimuli and weak or even negative effects emerging from naturally-occurring stimuli. Our study addresses these concerns by comparing several implementations of prominent sentence processing theories on an exploratory corpus and evaluating the most successful of these on a confirmatory corpus, using a new self-paced reading corpus of seemingly natural narratives constructed to contain an unusually high proportion of memory-intensive constructions. We show highly significant and complementary broad-coverage latency effects both for predictors based on the Dependency Locality Theory and for predictors based on a left-corner parsing model of sentence processing. Our results indicate that memory access during sentence processing does take time, but suggest that stimuli requiring many memory access events may be necessary in order to observe the effect.